Measurement errors are divided into systematic errors and random errors. The occurrence of mistakes is natural and unexpected. So we can't trust the result of a data point. Usually we collect multiple data points and pay great attention to how to select these samples to reduce the deviation.

2. Error handling

Statistics generally adopts three methods to analyze errors: statistical description, statistical reasoning and experimental design.

Statistical Description: Describe a set of data with charts and several summary figures (mean, variance and standard deviation).

Statistical inference: Determine when the difference between results may be caused by random error and when it cannot be attributed to random error. (Confidence Interval and Hypothesis Test)

Experimental design: Collect and analyze data to estimate the impact of process changes.

3. Continuous data and discrete data

Continuous data: continuously variable data, such as height and weight.

Discrete data: information such as area or classification, right or wrong.

4. Basic statistical terminology

Population: also called matrix, represented by n.

Sample: a subset of the population, represented by n.

Mean value: the average value, which is represented by U in the population and xbar in the sample.

Median: the middle number after sorting.

Variance: The population is represented by sigma square, and the sample is represented by s square. Note that the denominator is divided by n or n.

Standard deviation (Stdev): sigma is used for population and S is used for sample. Note that the denominator is divided by n- 1 or N- 1.

5. Normal distribution

This is the most common distribution in nature. For example, the height of people in a certain area and the size of parts produced by a certain machine. When studying normal distribution, we generally only need to take a few samples to grasp the overall trend.

Note that the standard normal distribution refers to a normal distribution with a mean of 0 and a standard deviation of 1.

Calculation of Z-value: We need to use the mean and standard deviation of normal distribution to transform it into "standard normal" distribution, so as to get the probability by using the standard normal distribution table.

Zusl =(USL-u)/ suitable horse; Zlsl =(LSL)/ Sigma

ZBench is the z value corresponding to the total probability of defects, which can be found from the normal table.

6. Central limit law

The central limit theorem shows that if n is large enough, whether a single variable obeys normal distribution or not, the distribution of sample mean (x) or its sum is similar to normal distribution.

7. Stiffness coefficient

After sorting the data, we can get Q 1 at14 and Q3 at 3/4, and the stability coefficient SF= Q 1/Q3.

With the decrease of deviation, the stability coefficient is closer to 1.0. .